We study the conditions required for $\chi_2 \to \chi + \tau^\pm \mu^\mp$
decays to yield observable tau flavour violation at the LHC, for cosmologically
interesting values of the neutralino relic density. These condition can be
achieved in the framework of a SU(5) model with a see-saw mechanism that allows
a possible coexistence of a LHC signal a low prediction for radiative LFV
decays.Comment: 7 pages, 5 figures, Prepared for the proceedings of the workshop:
  "LC09: $e^+ e^-$ Physics at the TeV Scale and the Dark Matter Connection",
  21-24 September 2009, Perugia, Ital

Carquin, E.

Gomez, M. E.

Naranjo, P.

Rodriguez-Quintero, J.

English

arXiv

We study the conditions required for χ2 → χ+τ±μ∓ decays to yield observable tau flavour violation at the LHC, for cosmologically interesting values of the neutralino relic density. These conditions can be achieved in the framework of a SU(5) model with a seesaw mechanism that allows a possible coexistence of a LHC signal with a low prediction for radiative LFV decays

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2010-10603-4Colloquia: LC09IL NUOVO CIMENTO Vol. 33 C, N. 2 Marzo-Aprile 2010τ-flavour violation at the LHCM. E. Gomez(1), E. Carquin(2), P. Naranjo(1) and J. Rodriguez-Quintero(1)(1) Departamento de F´ısica Aplicada, University of Huelva - Huelva, Spain(2) Departamento de F´ısica y Centro de Estudios Subato´micos, Universidad Te´cnica Feder´ıcoSanta Mar´ıa - Casilla 110-V, Valpara´ıso, Chile(ricevuto il 16 Marzo 2010; approvato il 15 Aprile 2010; pubblicato online il 18 Giugno 2010)Summary. — We study the conditions required for χ2 → χ+τ±μ∓ decays to yieldobservable tau flavour violation at the LHC, for cosmologically interesting values ofthe neutralino relic density. These conditions can be achieved in the framework of aSU(5) model with a seesaw mechanism that allows a possible coexistence of a LHCsignal with a low prediction for radiative LFV decays.PACS 11.30.Pb – Supersymmetry.PACS 11.30.Hv – Flavor symmetries.PACS 14.80.Ly – Supersymmetric partners of known particles.1. – IntroductionData from both atmospheric [1] and solar [2] neutrinos have by now confirmed theexistence of neutrino oscillations with near-maximal νμ−ντ mixing (Super-Kamiokande)and large νe → νμ one (SNO). These observations would also imply violation of thecorresponding charged-lepton numbers, which in supersymmetric theories might be sig-nificant and observable in low-energy experiments. Many signatures for charged-lepton-flavour violation have been considered [3, 4], including μ → eγ decays and conversions,τ → μγ and τ → eγ decays. Other possibilities that have been considered are the de-cays χ2 → χ + e±μ∓ [5], and χ2 → χ + μ±τ∓ [6, 7], where χ is the lightest neutralino,assumed here to be the lightest supersymmetric particle (LSP), and χ2 is the second-lightest neutralino. We present the results from [8] where we found that a signal forτ flavour-violating χ2 decays may be observable if the branching ratio exceeds about10%. We consider the cosmologically preferred parameter space (as dictated by WMAP)of b − τ Yukawa-unified models with massive neutrinos [9, 10]. We find that, assuminggeneral structures for the soft terms arising from a horizontal Abelian symmetry, SU(5)RGEs efficiently suppress off-diagonal terms in the scalar soft matrices [11] as comparedto the conventional case where the soft terms are postulated at the GUT scale, hencerendering the model compatible with current experimental bounds.c© Societa` Italiana di Fisica 9596 M. E. GOMEZ, E. CARQUIN, P. NARANJO and J. RODRIGUEZ-QUINTERO200 300 400 500 600 700 800 900M1/2  (GeV)01002003004005006007008009001000m0 (GeV)mh=114 GeVmh=111 GeVBR(b->s γ)=2.8  10 -4BR(b->s γ)=2.15  10 -4200 300 400 500 600 700 800 900M1/2 (GeV)01002003004005006007008009001000m0 (GeV)mh=114 GeVBR(b->s γ)=2.15 10 −4mh =111 GeVBR(b->s γ)=2.8 10 −4Fig. 1. – (Colour on-line) Cosmologically-favored areas (green) in the (M1/2,m0)-plane fortanβ = 35 and A0 = m0, assuming SU(5) unification. In the left panel we assume universalityat MX = MGUT, whereas in the right panel we assume universality at MX = 2×1017 GeV. Thered areas are excluded because mχ > mτ˜ . We also display the contours for mh = 111, 114GeV(black solid and thin solid) and BR(b → sγ) · 104 < 2.15, 2.85 (blue dashed and thin dashed).2. – Study of SUSY spectrum and parameter spaceWe pay particular attention to regions leading to large values of Γ(χ2 → χ+τ±+μ∓)via the on-shell slepton production mechanism:BR(χ2 → χτ±μ∓) =3∑i=1[BR(χ2 → l˜iμ)BR(l˜i → τχ)(1)+BR(χ2 → l˜iτ)BR(l˜i → μχ)],while satisfying all phenomenological and cosmological (relic density) constraints. Thecharacteristic parameter region for the signal in the τ channel to be optimal is definedby the following: i) mχ2 > mτ˜ > mχ; ii) one of the mass differences in i) is > mτ andthe other > mμ, mτ˜ > mχ, so that the μ, τ and τ˜ are all on-shell; iii) moderate valuesof mχ (phase space and luminosity considerations).Figure 1 is used to select points satisfying all phenomenological constraints for theevent analysis of the next section. In particular, for SU(5) unification and assuminguniversal soft terms at MX = 2×1017 GeV, tanβ = 35 is the smallest value of tanβ suchthat the WMAP area in the plane M1/2 −m0 is not excluded by the mh bound [10,9].In table I we display parameters of the two reference points A and B. Point A is theCMSSM model used in [6]. Point B is a model with universality assumed at a scale2 · 1017 GeV; for comparison with this point, we also present point C, a set of CMSSMparameters that leads to a similar sparticle spectrum and satisfies all the cosmologicaland phenomenological bounds. In all cases, we work with μ > 0.τ -FLAVOUR VIOLATION AT THE LHC 97Table I.Point Model type m0 M1/2 tanβ A0 Nevents σint LintA CMSSM 100 300 10 300 757K 25.3 pb 30 fb−1B SU(5) 40 450 35 40 730K 2.44 pb 300 fb−1C CMSSM 220 500 35 220 536K 1.79 pb 300 fb−13. – SUSY lepton flavour violationThe flavour mixing entries are defined as(2) δijXX = (M2XX)ij/(M2XX)ii (X = L,R).We take into account only 2–3 generation flavor mixing.In order to have significant LFV signals, we need Γ(χ2 → χ + τ± + μ∓)/Γ(χ2 →χ + τ± + τ∓) ∼ 0.1. Values of δLL leading to these ratios would imply a significantviolation of the τ → μγ bound. In fig. 2 we present the dependence of these decays onthe flavour mixing parameters δRR and δLL for point B. We see that in this case we needlarge non-diagonal entries in the slepton mass matrix in order to achieve a branchingratio for χ˜2 → χ˜1τ±μ∓ that is of interest for the LHC, e.g., δRR ∼ 0.15 for δLL = 0 orδLL ∼ 0.35 for δRR = 0. We also see that τ → μγ is very restrictive on the size of δLL,imposing a maximum value ∼ 0.03. We see in the bottom-right panel that δRR ∼ 0.15is allowed for δLL = 0. Due to the strong bound imposed by τ → μγ, it is very difficultto obtain reasonable values of δ using only the LL and/or RL mixing found in seesawmodels. However, significant FV entries on the RR sector can be generated only by usingnon-minimal models for the soft terms.0 0.1 0.2 0.3 0.4 0.5δRR00.10.20.30.40.50.60.70.80.91lfv/fc ratiosδLL=0δLL=0.30 0.1 0.2 0.3 0.4 0.5δRR10-910-810-710-610-510-4BR(τ−>μ γ)δLL=0δLL=0.3δLL=0.1δLL=0.2Exp. boundFig. 2. – Branching ratios for point B as functions of δRR for certain discrete choices of δLL.98 M. E. GOMEZ, E. CARQUIN, P. NARANJO and J. RODRIGUEZ-QUINTERO0 200 400 600 800 1000m0 (GeV)1e-131e-121e-111e-101e-091e-081e-071e-06BRτ −> μ γ, MX > MGUTτ −> e γ, MX > MGUTμ −> e γ, MX > MGUTτ −> μ γ, MX = MGUTτ −> e γ, MX = MGUTμ −> e γ, MX = MGUTtan β = 45, M1/2 = 1 TeV, A0 = 0.5Fig. 3. – Prediction for the charged-lepton flavour violating branching ratios showing the differ-ence of taking either MX or MGUT as the high scale.4. – SU(5) unification and GUT soft massesThe introduction of non-trivial flavour structures for the slepton soft terms at MGUT,although being reasonable as an implication of the family symmetry responsible for theYukawa texture, typically results on a large violation of the bounds on lj → liγ [12, 13].This picture may be remedied if we assume that SUSY is broken with universal softterms at a scale MX > MGUT. In this case, the cosmological requirement of havinga neutral particle as the LSP imposes low values on m0, such that mτ˜ > mχ [9, 10],since diagonal terms of the soft masses have a large RGE growth, while non-diagonalelements remain almost unaffected by the runs. Thus, even assuming non-diagonal softterms with matrix elements of the same order of magnitude at MX , the correspondingmatrix at MGUT exhibits dominant diagonal elements. To some extent, the RGE effectis similar to the action of closing an umbrella: the general non- universal soft terms atMX resemble an open umbrella that approaches a diagonal matrix at the GUT scale.In fig. 3, we show the differences respect considering: i) SU(5) RGE evolution of thesoft terms from the high scale MX down to MGUT and then the MSSM with seesawneutrinos (solid lines), ii) Soft SUSY breaking terms given at MGUT and then the MSSMwith seesaw neutrinos (dashed lines). In case ii) we stop the lines at the value of m0below which mτ˜ becomes the LSP. In contrast, m0 can even vanish at MX in case i). Weused the same textures and soft terms as in ref. [13]. However, unlike these authors, wedecouple the right-handed neutrinos below MGUT. As a result, the predicted BR’s donot vanish in the limit m0 = 0.We can provide one explicit example of the growth of the diagonal terms of theslepton mass matrix in models with interesting predictions for both LFV and Ωχh2. Letus consider the 0 < m0 < 100 GeV region. In the area of the parameter space whereτ -FLAVOUR VIOLATION AT THE LHC 990 20 40 60 80 100m0 (GeV)1e-131e-121e-111e-101e-091e-081e-071e-06BR(μ −> e γ)experimental upper boundtan β = 35, M1/2 = {350, 420} GeV, A0 = {0, 2}0 20 40 60 80 100m0 (GeV)1e-121e-111e-101e-091e-081e-071e-06BR(τ −> μ γ)experimental upper boundtan β = 35, M1/2 = {350, 420} GeV, A0 = {0, 2}0 20 40 60 80 100m0 (GeV)1e-081e-071e-06BR(τ −> e γ)experimental upper boundtan β = 35, M1/2 = {350, 420} GeV, A0 = {0, 2}Fig. 4. – Prediction for the lj → liγ branching ratios for the cosmologically preferred area ofvalues of M1/2, A0, for choice of U(1)F charges in ref. [11] leading to the matrices of eq. (5).WMAP bounds are satisfied due to τ − χ coannihilations, we find that m1/2 obeys alinear function of m0, m1/2 ∼ ai1 + ai2m0, where i runs over the multiplets. It turns outthat, taking into account that the radiative corrections to the off-diagonal entries of thesoft mass matrices are subdominant as compared with those of the diagonal ones, thesediagonal elements can be expressed as follows:(3) m2Si  C2i (m0)m20,where we have defined(4) C2i (m0) ≡14420πα5((ai1m0)2+2ai1ai2m0+ a22)ln(MXMGUT)and Si stands for the supermultiplets 10 and 5¯. As stated, eq. (3) implies a largeenhancement only of the diagonal entries of the soft matrices, thus further suppressingthe off-diagonal elements. It turns out indeed that for values of m0  60–80GeV at MXsuch an enhancement at the GUT scale is as large as  100. As a consequence, the softmass matrices m¯210 and m¯25 at GUT scale read as(5) m¯210 =⎛⎝ 1 ε3 ε5ε3 1 ε4ε5 ε4 1⎞⎠C2(m0)m20, m¯25 =⎛⎝0 0 00 1 ε30 ε3 1⎞⎠C2(m0)m20which clearly exhibit the suppression on the off-diagonal terms (compare with textures).The corresponding predictions for LFV radiative decays at tanβ = 35 are displayed infig. 4.5. – SUSY-LFV events at the LHCThe spectra for points of table I were calculated using ISAJET 7.78 [14] and theninterfaced into PYTHIA 6.418 [15]. The SUSY-LFV decays described in the previous100 M. E. GOMEZ, E. CARQUIN, P. NARANJO and J. RODRIGUEZ-QUINTEROFig. 5. – (Colour on-line) Visible lτh mass distributions with OS (red solid lines), SS (greendashed lines), and OS Standard Model backgrounds (shaded). The LFV OS μτh pairs are alsoshown (pink-dot-dashed). Left plot is for case A and right plot for case B.sections give a μ±τ∓ pair and produce an asymmetry between μ±τ∓ and e±τ∓ finalstates that would not be observable in the case of charged lepton number conservation.In fig. 5, an excess of OS l∓τ±h pairs over the SS pairs can be seen. The left (right) plotcorresponds to point A (B) and shows the numbers of events normalized to a referenceluminosity of 10 fb−1 (100 fb−1). The observable numbers, NLFVμτh , of μ∓τ±h LFV pairsare obtained by summing the counts in the subtracted μ∓τ±h − e∓τ±h distributions in theinterval of Mlτ masses between 30 and 110GeV. We obtainPoint A : NLFVμτh = 470± 39 (12 σ),(6)Point B : NLFVμτh = 308± 30 (10 σ),where we quote only the statistical errors for the signal samples. If we estimate anefficiency of 70% for the jet-tau matching, the signal is reduced to 10σ for point Aand 9σ for point B. Therefore, LFV signal has a good likelihood of being observable, aslong as its branching ratio exceeds about 10%.6. – ConclusionsThe observation of LFV in neutralino decays at the LHC can be possible ifΓ(χ2 → χ1τ±μ∓)/Γ(χ2 → χ1τ±τ∓) ∼ 0.1. The LFV signal remains observable at pointswhich are favoured in the usual CMSSM framework. Finally, we conclude that the searchfor this decay at the LHC is interesting and complementary to the parallel searches forτ → μγ decays, for non-minimal GUTs. Furthermore, linear colliders will allow to explorecomplementary parameter space [16].As a final remark, let us stress that the phenomenological analysis performed in thiswork can naturally be embedded within a SU(5) GUT model featuring non-universalsoft terms at the high scale MX , whose origin can be traced back to a U(1)F familysymmetry [11].τ -FLAVOUR VIOLATION AT THE LHC 101∗ ∗ ∗The work of EC has been partly supported by the MECESUP Chile Grant and theHELEN Program. MEG and JRQ are supported by the Spanish MICINN projectsFPA2009-10773, FPA2008–04063–E/INFN and the project P07FQM02962 funded by“Junta de Andalucia”.REFERENCES[1] Fukuda Y. et al. (Super-Kamiokande Collaboration), Phys. Rev. Lett., 81 (1998)1562.[2] Fukuda Y. et al. (Super-Kamiokande Collaboration), Phys. Rev. Lett., 82 (1999)1810; 2430; Ahmad Q. R. et al. (SNO Collaboration), Phys. Rev. Lett., 87 (2001)071301.[3] Kuno Y. and Okada Y., Rev. Mod. Phys., 73 (2001) 151.[4] Ellis J., Gomez M. E. and Lola S., JHEP, 0707 (2007) 052.[5] Hisano J., Nojiri M. M., Shimizu Y. and Tanaka M., Phys. Rev. D, 60 (1999) 055008.[6] Hinchliffe I. and Paige F. E., Phys. Rev. D, 63 (2001) 115006.[7] Carvalho D., Ellis J., Gomez M., Lola S. and Romao J., Phys. Lett. B, 618 (2005)162.[8] Carquin E., Ellis J., Gomez M. E., Lola S. and Rodriguez-Quintero J., JHEP,0905 (2009) 026.[9] Gomez M. E., Lola S., Naranjo P. and Rodriguez-Quintero J., JHEP, 0904 (2009)043.[10] Calibbi L., Mambrini Y. and Vempati S. K., JHEP, 0709 (2007) 081.[11] Gomez M. E., Lola S., Naranjo P. and Rodriguez-Quintero J., (in preparation).[12] Leontaris G. K. and Tracas N. D., Phys. Lett. B, 431 (1998) 90; Gomez M. E.,Leontaris G. K., Lola S. and Vergados J. D., Phys. Rev. D, 59 (1999) 116009.[13] Chankowski P. H., Kowalska K., Lavignac S. and Pokorski S., arXiv:hep-ph/0507133.[14] Baer H., Paige F. E., Protopopescu S. D. and Tata X., arXiv:hep-ph/0312045.[15] Sjostrand T., Mrenna S. and Skands P., JHEP, 05 (2006) 026 (LU TP 06-13,FERMILAB-PUB-06-052-CD-T).[16] Carquin E., Ellis J., Gomez M. E., Lola S. and Rodriguez-Quintero J., (inpreparation).

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